One known HF flexible antenna is utilized in a wrist watch which has the particular feature that it is controlled by radio signals, which are synchronized by a precision atomic master clock. In order to provide for the flexibility of the HF antennas the magnetic core is built up of a plurality of thin flexible layers of amorphous metallic glass. The antenna winding consists of thin copper wire, which is wrapped around the magnetic core in a plurality of layers. At the winding itself the magnetic core is not flexible so that it is not possible to greatly increase the number of turns of the coil. In fact, if the winding has a great length in the direction of the magnetic core axis, the magnetic core will be stiff in a substantial part thereof so that it can not be bent without the risk of damage. Furthermore, the copper wire winding wrapped around the magnetic core is responsible for a substantial increase in the thickness of the core adjacent to said winding, so that such an antenna may not be utilized for applications where a particularly thin configuration is necessary.